Ads Lab Manual

ADVANCED DATA STRUCTURES – LAB MANUAL

ADVANCED DATA STRUCTURES LAB MANUAL

E. Vijaya Kumar, M. Tech, M.I.S.T.E.

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INDEX

S.NO NAME OF THE EXERCISE

PAGE

Stack ADT using arrays

2

Queue ADT using arrays

5

Stack ADT using linked lists

9

Queue ADT using linked lists

13

Deque using stack

18

Deque using doubly linked list

25

Binary Search Tree- Operations

30

Tree Traversals

35

Graph-DFS

40

Graph-BFS

43

Merge sort

47

Heap Sort

51


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INDEX

S.NO NAME OF THE EXERCISE

PAGE

Stack ADT using arrays

2

Queue ADT using arrays

5

Stack ADT using linked lists

9

Queue ADT using linked lists

13

Deque using stack

18

Deque using doubly linked list

25

Binary Search Tree- Operations

30

Tree Traversals

35

Graph-DFS

40

Graph-BFS

43

Merge sort

47

Heap Sort

51


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B-Tree- Insertion & Deletion

AVL Tree- Insertion & Deletion

54

58

Kruskal’s Algorithm

70

Prim’s Algorithm

74

Dictionary ADT using hashing

78


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1)

Writ Wr ite e a C++ C++ pro progr gram am to impl implem emen entt sta stack ck ADT ADT usi using ng arra arrays ys.. AIM: To write a C++ program to implement stack ADT using arrays. ALGORITHM: 1. Push ( ) 1. 2. 3. 4. 5.

start read n if top top grea greater ter than than (n-1) (n-1) then then prin printt “ove “overf rflo low” w” else 6. toptop+1 7. data ata[top [top]= ]=d d 8. print print “elem “element ent pushe pushed d to stack” stack” 9. stop.

2. Pop( ) 1. 2. 3. 4.

start if top< top< 0 then then prin printt “un “unde derf rflo low” w” else 5. ddata[top] 6. toptop-1 7. print print “elem “element ent is popped popped from the stack” stack” 8. stop.

PROGRAM: #include #include #define size 15 template class stack { T top,stk[size]; top,stk[size]; public: stack(); void push(T n); T pop(); }; template stack::stack() { top=0; E. Vijaya Kumar, M. Tech, M.I.S.T.E.

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} template void stack::push(T n) { if (top==size) {cout<<"\n stack is full"; } stk[top]=n; top++; } template stack::pop() { if(top==NULL) { cout<<"\n stack is empty\n"; } top--; return(stk[top]); } void main() { stack ob; int i=0; clrscr(); cout<<"elements of stack"<
OUTPUT: E. Vijaya Kumar, M. Tech, M.I.S.T.E.

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elements of stack pushed element 0 pushed element 1 pushed element 2 pushed element 3 pushed element 4 pushed element 5 pushed element 6 pushed element 7 pushed element 8 pushed element 9 pushed element 10 pushed element 11 pushed element 12 pushed element 13 pushed element 14 elements out of stack popped out element is 14 popped out element is 13 popped out element is 12 popped out element is 11 popped out element is 10


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2)

Write a C++ program to implement queue ADT using arrays. AIM: To write a C++ program to implement queue ADT using arrays.

ALGORITHM: 1. Insertion( ) 1. start 2. read n 3. if rear== (n-1) then 4. print “overflow” 5. print “enter a number” 6. read num 7. if front == -1 then 8. front=rear=0 9. else 10. rear=rear+1 11. a[rear]=num 12. print”number is inserted” 13. stop 2. Deletion( ) 1. start 2. if front == -1 then 3. print “underflow” 4. print “deleted element is” 5. print a[front] 6. if front==rear then 7. front=rear=-1 8. else 9. front=front+1 10. print “number is deleted” 11. stop. PROGRAM: #include #include #include const int size=10; int rear=-1,front=0; template E. Vijaya Kumar, M. Tech, M.I.S.T.E.

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class queue { T qa[size]; T temp; public: int empty(void); int full(void); void insert(T x); T delet(void); void disp(); }; template int queue::empty(void) queue::empty(void) { if(front>rear) return(0); else return 1; } template int queue::full(void) queue::full(void) { if(rear>size-1) return 0; else return 1; } template void queue::insert(T x) { qa[++rear]=x; cout< T queue::delet() queue::delet() { return (qa[front++]); (qa[front++]); } template void queue::disp() { if(front>rear) cout<<"queue is empty"<=front;i--) i=rear;i>=front;i--) cout<
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} void main() { int p; int v; queue q; clrscr(); q.empty(); q.full(); q.insert(5); q.delet(); q.disp(); getch(); } OUTPUT: *************MENU************ 1.Insert 2.Delete 3.Display 4.Quit Enter Ur Choice 1 Enter size 3 Enter elements 12 13 14 *************MENU************ 1.Insert 2.Delete 3.Display 4.Quit Enter Ur Choice 2 12 13 14 *************MENU************ 1.Insert 2.Delete 3.Display 4.Quit Enter Ur Choice 3 E. Vijaya Kumar, M. Tech, M.I.S.T.E.

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deleted element is 12 *************MENU************ 1.Insert 2.Delete 3.Display 4.Quit Enter Ur Choice 3 deleted element is 13

3) Writ Wr ite e a C++ C++ Prog Progra ram m to to imp imple leme ment nt a Sta Stack ck ADT ADT usin using g a sin singl gly y linked list AIM:


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To write a C++ program to implement a Stack ADT using a singly linked list. ALGORITHM: 1. Push (d) 1. start 2. *n is a new new node node 3. read num 4. nd = num 5. n  next = top 6. top=n 7. print nu num 8. print print “is “is push pushed ed to to stack stack”” 9. stop. 2. Pop ( ) 1. start 2. if top top == == NUL NULL L the then n 3. prin printt “un “unde derf rflo low” w” 4. num= topd 5. *d is the the new new node node 6. d=top 7. top=topnext 8. deleted 9. stop. PROGRAM: #include #include #include class stak { struct stks { int data; stks *next; }; stks *p,*temp,*top; public: stak() { top = NULL; } push(); pop(); E. Vijaya Kumar, M. Tech, M.I.S.T.E.

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disp(); }; stak::push() { clrscr(); temp= new stks; cout<<"enter a value \n"; cin>>temp->data; if(top==NULL) { top = temp; temp->next=NULL; } else { temp->next=top; top=temp; } cout<<"the element inserted = "<data<next; cout<<"element iremoved = "<data; delete p; } return 0;} stak::disp() { if(top==NULL) cout<<"stack is empty\n"; else { p=top; cout<<"stack contains \n"; while(p!=NULL) { cout<data<<" "; p=p->next; } }return 0; } void main() { stak s1; E. Vijaya Kumar, M. Tech, M.I.S.T.E.

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int ch,l; clrscr(); cout<< "stack operations using Linked list\n"; while(l) { cout<<"\n 1. PUSH\n"; cout<<"2.POP\n"; cout<<"3.DISPLAY\n"; cout<<"4.quit\n"; cout<<"enter Ur choice\n"; cin>>ch; switch(ch) { case 1: s1.push(); break; case 2: s1.pop(); break; case 3: s1.disp(); break; default: exit(0); }}}

OUTPUT: stack operations using Linked list 1. PUSH E. Vijaya Kumar, M. Tech, M.I.S.T.E.

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2.POP 3.DISPLAY 4.quit enter Ur choice 1 enter a value 12 the element inserted = 12 1. PUSH 2.POP 3.DISPLAY 4.quit enter Ur choice 1 enter a value 13 the element inserted = 13

4)

1. PUSH 2.POP 3.DISPLAY 4.quit enter Ur choice 3 stack contains 13 12 1. PUSH 2.POP 3.DISPLAY 4.quit enter Ur choice 2 element iremoved = 13 1. PUSH 2.POP 3.DISPLAY 4.quit enter Ur choice 2 Write a C++ program to implement a queue ADT using a singly linked list. AIM: To write a C++ program to implement a queue ADT using a singly linked list.


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ALGORITHM: 1. Insertion ( ) 1.1.start 1.2. *link is a new node 1.3. read num 1.4. *new is a new node ndata=num //storing the data 1.5. 1.6. nlink = NULL //storing the address 1.7.If front == NULL then 1.7.1 Front = rear=n 1.7.2 Print “number is inserted” 1.7.3 Return 1.8. rearlink =n 1.9. rear=n 1.10. print “number is inserted” 2. Deletion ( )

.1 .2 .1 .2 .3

.1start .2 *d is a new node .3 if front == NULL then print “underflow” return .4 if front is equal to rear then front = rear = NULL print “ no. is deleted” return .5 d=front .6 front=front link print ddata .7 .8 print “is deleted” .9 deleted .10 stop.

PROGRAM: #include #include #include


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class rque { struct node { int data; node *link; }*fr,*re; public: rque(); void addq(int item); int delq(); void disp(); // ~rque(); }; rque::rque() { fr=re=NULL; } void rque::addq(int item) { node *temp; temp=new node; if(temp==NULL) cout<<"Queue is full\n"; temp->data=item; temp->link=NULL; if(fr==NULL) { re=fr=temp; return; } re->link=temp; re=re->link; } int rque::delq() { if(fr==NULL) { cout<<"\nQueue is empty\n"; return NULL; } else {node *temp; int item; item=fr->data; temp=fr; fr=fr->link; E. Vijaya Kumar, M. Tech, M.I.S.T.E.

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delete temp; return item;} } /* rque::~rque() { if(fr==NULL) return; node *temp; while(fr!=NULL) { temp=fr; fr=fr->link; delete temp; } } */ void rque::disp() { while(fr!=NULL) {cout<data<<"\n"; fr=fr->link; } } void main() { rque rq; int i,size,a[10],ch=1; clrscr(); while(ch!=5) { cout<<"\n *************MENU***********\n"; cout<<" 1.Insert\n"; cout<<" 2.Display\n"; cout<<" 3.Delete\n"; cout<<" 4.Quit\n"; cout<<"Enter Ur Choice\n"; cin>>ch; switch(ch) { case 1: { cout<<"\n enter the size of the queue\n"; cin>>size; cout<<"Enter elements\n"; for(i=0;i>a[i]; rq.addq(a[i]); } break; } E. Vijaya Kumar, M. Tech, M.I.S.T.E.

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case 2: { cout<<"Display list\n"; rq.disp();break; } case 3: { cout<<"Delete process\n"; int j=rq.delq(); cout<<"Extracted element is "<
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13 14 15 *************MENU*********** 1.Insert 2.Display 3.Delete 4.Quit Enter Ur Choice 3 Delete process Queue is empty Extracted element is 0 *************MENU*********** 1.Insert 2.Display 3.Delete 4.Quit Enter Ur Choice

5)

Write a C++ program to implement the deque( doubly ended queue ) ADT using a stack. AIM: To write a c++ program to implement deque ADT using a stack. ALGORITHM: 1.Insertion_Front() 1. start


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2. if front == 0 & rear==-1 a. d[front]==x b. rear++ 3. if front == 0 & rear != -1 a. print “insertion not possible” 4. else a. f-b. dq[f]=x 5. print “ no. is inserted” 2.Deletion_Front() 1. 2. 3. 4. 5.

start if rear = = -1 print “queue is empty” else if(front = = rear) a. rear=-1; b. front=0; 6. else 7. front++; 8. print “ deleted” 3.Insertion_Rear() 1. 2. 3. 4.

start if(r==n-1) print “Queue Is Full” else a. r++; b. dq[r]=x; 5. print “inserted”

4.Deletion_Rear () 1. 2. 3. 4. 5.

start if rear == -1 print “Queue is empty” else if front == rear a. front =0 b. rear=-1 6. print “deleted” PROGRAM: E. Vijaya Kumar, M. Tech, M.I.S.T.E.

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// Program De queue #include #include #define n 3 template class dqueue { private: t dq[n],x; int i,j,f,r; public: dqueue() { f=0; r=-1; } void insert_rear(); void insert_front(); void del_rear(); void del_front(); void show(); }; template void dqueue::insert_rear() { if(r==n-1) cout<<"\t\t\tQUEUE IS FULL"; else { char ch='y'; while(ch=='y') { cout<<"ENTER THE DATA:"; cin>>x; r++; dq[r]=x; cout<<"\t\tANY MORE DATA(y/n):"; cin>>ch; } } } template void dqueue::insert_front() { E. Vijaya Kumar, M. Tech, M.I.S.T.E.

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if((r==-1) && (f==0)) { dq[f]=x; r++; } else { if((f==0) && (r!=-1)) cout<<"\t\tNOT POSSIBLE TO INSERT"; else { char ch='y'; while(ch=='y') { if(f==0) cout<<"\t\tNOT POSSIBLE TO INSERT"; else { cout<<"\t\tENTER THE DATA:"; cin>>x; f--; dq[f]=x; cout<<"\t\tANY MORE DATA(y/n):"; cin>>ch; } } } } } template void dqueue::del_rear() { if(r==-1) cout<<"\t\t\tQUEUE IS EMPTY"; else { if(f==r) { f=0; r=-1; show(); } else { r--; show(); } E. Vijaya Kumar, M. Tech, M.I.S.T.E.

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} } template void dqueue::del_front() { if(r==-1) cout<<"\t\t\tQUEUE IS EMPTY"; else { if(f==r) { r=-1; f=0; show(); } else { f++; show(); } } } template void dqueue::show() { if(r==-1) cout<<"\t\t\tQUEUE IS EMPTY"; else { cout<<"\n\t\tTHE ELEMENTS ARE:"<<"\n\n\t\t\t"; for(i=f;i<=r;i++) cout< void dq_op(dqueue dq) { int choice; do { cout<<"\n1.INSERT_REAR"<<"\n"; cout<<"2.INSERT_FRONT"<<"\n"; cout<<"3.DELETE_REAR"<<"\n"; cout<<"4.DELETE_FRONT"<<"\n"; cout<<"5.SHOW"<<"\n"; cout<<"6.EXIT"<<"\n"; cout<<"ENTER THE CHOICE:"; E. Vijaya Kumar, M. Tech, M.I.S.T.E.

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cin>>choice; switch(choice) { case 1:dq.insert_rear();break; case 2:dq.insert_front();break; case 3:dq.del_rear();break; case 4:dq.del_front();break; case 5:dq.show();break; case 6:break; } }while(choice!=6); }

main() { clrscr(); int ch; do { cout<<"\n1.INT"<<"\n"; cout<<"2.CHAR"<<"\n"; cout<<"3.EXIT"<<"\n"; cout<<"ENTER THE CHOICE:"; cin>>ch; switch(ch) { case 1: dqueue i; int x1; dq_op(i); break; case 2: dqueue c; char x2; dq_op(c); break; case 3:break; } }while(ch!=3); } OUTPUT: 1.INT 2.CHAR E. Vijaya Kumar, M. Tech, M.I.S.T.E.

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3.EXIT ENTER THE CHOICE:1 1.INSERT_REAR 2.INSERT_FRONT 3.DELETE_REAR 4.DELETE_FRONT 5.SHOW 6.EXIT ENTER THE CHOICE:1 ENTER THE DATA:12 ANY MORE DATA(y/n):y ENTER THE DATA:13 ANY MORE DATA(y/n):n 1.INSERT_REAR 2.INSERT_FRONT 3.DELETE_REAR 4.DELETE_FRONT 5.SHOW 6.EXIT ENTER THE CHOICE:5 THE ELEMENTS ARE: 12 13 1.INSERT_REAR 2.INSERT_FRONT 3.DELETE_REAR 4.DELETE_FRONT 5.SHOW 6.EXIT ENTER THE CHOICE:3 THE ELEMENTS ARE: 12 1.INSERT_REAR 2.INSERT_FRONT 3.DELETE_REAR 4.DELETE_FRONT 5.SHOW 6.EXIT ENTER THE CHOICE:


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6)

Write a C++ program to implement the deque ( doubly ended queue ) ADT using a doubly linked list AIM: To write a C++ program to implement the deque ADT using a doubly linked list. ALGORITHM: I. Insertion ( ): 1. start 2. * link is a new node 3. read num 4. * n is a new node 5. n → data = num 6. n → link = NULL 7. if front == NULL then


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7.1 front = rear = n 7.2 print “no is inserted 7.3 return 8. rear → link = n 9. rear = n 10. print “no is inserted” II. Deletion ( ): 1. start 2. * d is a new node 3. if front is equal to NULL then 3.1 print “underflow” 3.2 return 4. front is equal to rear then 4.1 front = rear = NULL 4.2 print “no is deleted 4.3 return 5. d = front 6. front = front → link 7. print d → data 8. print “ is deleted” 9. delete d 10. stop

PROGRAM: #include #include template class node { node *prev; T data; node *next; public: friend class Doub; }; template class Doub { node *fr; public: Doub(){fr = 0;} ~Doub(); E. Vijaya Kumar, M. Tech, M.I.S.T.E.

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void create(); void insert(int , T); void Delete(int, T &); void disp(); }; template Doub::~Doub() { node *p=fr; node *q; while(p) { q=p; p=p->next; delete q; cout<<"object destsroyed"< void Doub:: create() { T data; char ch; do {cout<<"Enter the data element"; cin>>data; if (fr==0) { fr=new node; fr->prev=0; fr->data=data; fr->next=0; } else { node *q=fr,*r; while(q->next!=0) { q=q-> next; } r=new node; r->data=data; r->next=0; r->prev=q; q->next=r; } cout<<"Do you want to continue(Y/N)"; cin>>ch; }while(ch=='Y'||ch=='y'); } E. Vijaya Kumar, M. Tech, M.I.S.T.E.

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template void Doub::insert(int pos,T data) { node *q,*temp; if(pos==0) { temp=new node; temp->prev=0; temp->data=data; temp->next=fr; fr=temp; } else { node *p=fr; for(int i=0;inext; if(p) { temp=new node; temp->data=data; p->prev->next=temp; temp->next=p; p->prev=temp; } else cout<<"Invalid position entered"; } } template void Doub::Delete(int pos,T &data) { node *p=fr; if (pos==0) { fr=fr->next; fr->prev=0; data=p->data; delete p; } else { for(int k=0; knext; data=p->data; if(p->next==NULL) p->prev->next=NULL; else { E. Vijaya Kumar, M. Tech, M.I.S.T.E.

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p->next->prev=p->prev; p->prev->next=p->next; } delete p; } } template void Doub:: disp() { node *curr=fr; cout<data<<"->"; curr=curr->next; }} void main() { Doub obj; int pos,data; clrscr(); cout<<"create method is invocked"<>pos>>data; obj.insert(pos,data); cout<<"Display"<>pos>>data; obj.Delete(pos,data); cout<<"Display after Delete"; obj.disp(); getch(); } OUTPUT: create method is invoked Enter the data element2 Do you want to continue(Y/N)y Enter the data element3 Do you want to continue(Y/N)y Enter the data element4 E. Vijaya Kumar, M. Tech, M.I.S.T.E.

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Do you want to continue(Y/N)y Enter the data element5 Do you want to continue(Y/N)n Display 2->3->4->5->Enter the position & data3 67 Display 2->3->4->67->5->enter element position to be deleted 5 5 Display after Delete 2->3->4->67->5->object destroyed

7)

Write a C++ program to perform the following operations. a. Insert an element into binary search tree b. Delete an element from binary search tree c. Search fr a key element in binary search tree. AIM: To write a c++ program to implement a Binary search tree. ALGORITHM: inorder ( node * r) : 1. start 2. if ptr ! = NULL then 3. in order (ptr → LC) 4. print data (ptr) 5. in order (ptr → RC) 6. stop PROGRAM: #include #include #define TRUE 1 #define FALSE 0


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class btree { struct btnode { btnode *left; int data; btnode *right; }*root; public: btree(); void create(int num); static void insert(btnode **sr,int); static void search(btnode **sr,int num,btnode **par,btnode **x,int *found); void remove(int num); static void rem(btnode **sr,int num); void disp(); static void inorder(btnode *sr); ~btree(); static void del(btnode *sr); }; btree::btree() { root=NULL; } void btree::create(int num) { insert(&root,num); } void btree::insert(btnode **sr,int num) { if(*sr==NULL) { *sr=new btnode; (*sr)->left=NULL; (*sr)->data=num; (*sr)->right=NULL; } else { if(num<(*sr)->data) insert(&((*sr)->left),num); else insert(&((*sr)->right),num); }} void btree::remove(int num) { rem(&root,num); } void btree::rem(btnode **sr,int num) E. Vijaya Kumar, M. Tech, M.I.S.T.E.

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{ int found; btnode *parent,*x,*xsucc; if(*sr==NULL) { cout<<"\n Tree is empty"; return; } parent=x=NULL; search(sr,num,&parent,&x,&found); if(found==FALSE) { cout<<"\n data to be deleted, not found"; return; } if(x->left!=NULL&&x->right!=NULL) { parent=x; xsucc=x->right; while(xsucc->left!=NULL) { parent=xsucc; xsucc=xsucc->left; } x->data=xsucc->data; x=xsucc; } if(x->left==NULL&&x->right==NULL) { if(parent->right==x) parent->right=NULL; else parent->left=NULL; delete x; return; } if(x->left==NULL&&x->right!=NULL) { if(parent->left==x) parent->left=x->right; else parent->right=x->right; delete x; return; } if(x->left!=NULL&&x->right==NULL) { if(parent->left==x) E. Vijaya Kumar, M. Tech, M.I.S.T.E.

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parent->left=x->left; else parent->right=x->left; delete x; return; }} void btree::search(btnode **sr,int num,btnode **par,btnode **x,int *found) { btnode *q; q=*sr; *found=FALSE; *par=NULL; while(q!=NULL) { if(q->data==num) { *found=TRUE; *x=q; return; } *par=q; if(q->data>num) q=q->left; else q=q->right; }} void btree::disp() { inorder(root); } void btree::inorder(btnode *sr) { if(sr!=NULL) { inorder(sr->left); cout<data<<"\t"; inorder(sr->right); }} btree::~btree() { del(root); } void btree::del(btnode *sr) { if(sr!=NULL) { del(sr->left); del(sr->right); E. Vijaya Kumar, M. Tech, M.I.S.T.E.

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} delete sr; } void main() { btree bt; char ch='y'; int req,i=0,size,num,a[10],elm; clrscr(); cout<<"Enter size of the tree\n"; cin>>size; cout<<"enter elements\n"; while(i<=size) { cin>>a[i]; bt.create(a[i]); i++; } cout<<"\nBtree before deletion \n"; bt.disp(); while(ch=='y') { cout<<"enter deleting elem\n"; cin>>elm; bt.remove(elm); cout<<"\nBinary tree after delete\n"; bt.disp(); cout<<"do you want delete ?\n"; cin>>ch; } getch(); }

OUTPUT: Output Enter size of the tree 3 enter elements 34 23 12 56


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Btree before deletion 12 23 34 56 enter deleting elem 34 Binary tree after delete 12 23 56 do you want continue ? n

8)

Write a C++ program that uses non-recursive functions to traverse the given binary tree a. Preorder b. Postorder c. Inorder AIM: A c++ program to create a binary tree and traverse it inorder, preorder, and postorder. ALGORITHM: I. build ( ): 1. start 2. read num 3. if num is equal to zero then 3.1 root = NULL 4. root = new node 5. root → data = num 6. root → lptr = root → rptr = NULL 7. read num 8. while num ! = 0 then 8.1 n = new node 8.2 n → data = num 8.3 n → lptr = n → rptr = NULL 8.4 s = root


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8.5 while s! = NULL 8.6 c = s 8.6.1 if num > s → data 8.6.2 s = s → rptr 8.6.3 else 8.6.4 s = s → lptr 8.6.5 if num > c → data 8.6.6 c →rptr = n 8.6.7 else 8.6.8 c → lptr = n 8.6.9 read num 9. stop II.Inorder ( node * r) : 1. start 2. if ptr ! = NULL then 3. in order (ptr → LC) 4. print data (ptr) 5. in order (ptr → RC) 6. stop III.Preorder ( node * r) : 1. start 2. if ptr ! = NULL then 3. print data (ptr) 5. pre order (ptr → LC) 4. pre order (ptr → RC) 5. stop IV.Postorder ( node * r) : 1. start 2. if ptr ! = NULL then 3. post order (ptr → LC) 4. post order (ptr → RC) 5. print data (ptr) 6. stop

PROGRAM #include #include E. Vijaya Kumar, M. Tech, M.I.S.T.E.

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class btre { struct bnode { bnode *lc; int data; bnode *rc; }*root; public: btre(); void ctree(int num); static void insert(bnode **sr,int num); void traverse(); static void inorder(bnode *sr); static void preorder(bnode *sr); static void postorder(bnode *sr); static void del(bnode *sr); ~btre(); }; btre::btre() { root=NULL; } void btre::ctree(int num) { insert(&root,num); } void btre::insert(bnode **sr,int num) { if(*sr==NULL) { *sr=new bnode; (*sr)->lc=NULL; (*sr)->data=num; (*sr)->rc=NULL; return; } else { if(num<(*sr)->data) insert(&((*sr)->lc),num); else insert(&((*sr)->rc),num); } return; } void btre::traverse() { cout<<"Inordertra\n"; inorder(root); cout<<"\npre order\n"; E. Vijaya Kumar, M. Tech, M.I.S.T.E.

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preorder(root); cout<<"\npost order \n"; postorder(root); } void btre::inorder(bnode *sr) { if(sr!=NULL) { inorder(sr->lc); cout<<"\t"<data; inorder(sr->rc); } else return; } void btre::preorder(bnode *sr) { if(sr!=NULL) { cout<<"\t"<data; preorder(sr->lc); preorder(sr->rc); } else return; } void btre::postorder(bnode *sr) { if(sr!=NULL) { postorder(sr->lc);postorder(sr->rc); cout<<"\t"<data; } else return; } btre::~btre() { del(root); } void btre::del(bnode *sr) { if(sr!=NULL) { del(sr->lc); del(sr->rc); } delete sr; E. Vijaya Kumar, M. Tech, M.I.S.T.E.

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} void main() { btre bt; int req,i=1,num; clrscr(); cout<<"specify the no of items to be inserted \n"; cin>>req; while(i++<=req) { cout<<"enter the data \n"; cin>>num; bt.ctree(num); } bt.traverse(); getch(); }

OUTPUT: specify the no of items to be inserted 5 enter the data 12 enter the data 23 enter the data 34 enter the data 11 enter the data 45 Inorder 11 12 23 pre order 12 11 post order 11 45

34

45

23

34

45

34

23

12


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9) Write a C++ program for the implementation of dfs for a given graph AIM: A c++ program to implement the depth first search algorithm for the given graph. ALGORITHM: I. DFS (int i) 1. start 2. visited [i] = 1 3. print “Node visited” 4. print i = i + 1 5. for j = 0 to max size 5.1 if ((visisted [j] ==0) && graph [i][j] ==1)) 5.2 dfs(j); 6. stop PROGRAM: #include #include #define TRUE 1 #define FALSE 0 const int MAX=8; struct node { int data; node *next; }; E. Vijaya Kumar, M. Tech, M.I.S.T.E.

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class graph { int visit[MAX]; public: graph(); void dfs(int v,node **p); node *getn(int val); void del(node *n); }; graph::graph() { for(int i=0;idata-1]==FALSE) dfs(t->data,p); else t=t->next; } } node *graph::getn(int val) { node *newnode=new node; newnode->data=val; return newnode; } void graph::del(node *n) { node *temp; while(n!=NULL) { temp=n->next; delete n; n=temp; } } void main() { node *arr[MAX]; node *v1,*v2,*v3,*v4; graph g; E. Vijaya Kumar, M. Tech, M.I.S.T.E.

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clrscr(); v1=g.getn(2); arr[0]=v1; v1->next=v2=g.getn(3); v2->next=NULL; v1=g.getn(1); arr[1]=v1; v1->next=v2=g.getn(4); v2->next=v3=g.getn(5); v3->next=NULL; v1=g.getn(1); arr[2]=v1; v1->next=v2=g.getn(6); v2->next=v3=g.getn(7); v3->next=NULL; v1=g.getn(2); arr[3]=v1; v1->next=v2=g.getn(8); v2->next=NULL; v1=g.getn(2); arr[4]=v1; v1->next=v2=g.getn(8); v2->next=NULL; v1=g.getn(3); arr[5]=v1; v1->next=v2=g.getn(8); v2->next=NULL; v1=g.getn(3); arr[6]=v1; v1->next=v2=g.getn(8); v2->next=NULL; v1=g.getn(4); arr[7]=v1; v1->next=v2=g.getn(5); v2->next=v3=g.getn(6); v3->next=v4=g.getn(7); v4->next=NULL; cout<

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dfs format is :1 2 4

8

5

6

3

7

Graph after deletion

10)

Write a C++ program for the implementation of bfs for a given graph.

AIM: A c++ program to implement the breadth first search algorithm for the given graph. ALGORITHM: 1. bfs (int) : 1. start 2. visited [i] = 1 3. addq [i] 4. while front ! = rear 4.1 i = deleteq ( ) 4.2 i = i + 1 5. for j = 0 to max size 6. if visited [j] ==0 && graph [i][j] == 1 then 6.1 addq (i) 6.2 visited [j] = 1 7. j = j+1 8. stop PROGRAM: #include #include #include #define TRUE 1 #define FALSE 0 const int MAX=8; struct node { E. Vijaya Kumar, M. Tech, M.I.S.T.E.

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int data; node*next; }; class graph { private: int visited[MAX]; int q[8]; int front, rear; public: graph(); void bfs(int v, node **p); node *getnode_write(int val); static void addqueue(int *a, int vertex,int *f, int *r); static int deletequeue(int *q,int *f,int *r); static int isempty(int *f); void del(node *n); }; graph::graph() { for(int i=0;idata-1]==FALSE) { addqueue(q,u->data,&front,&rear); visited[u->data-1]=TRUE; cout<data<<"\t"; } u=u->next; } } } node *graph::getnode_write(int val) E. Vijaya Kumar, M. Tech, M.I.S.T.E.

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{ node *newnode=new node; newnode->data=val; return newnode; } void graph::addqueue(int *a,int vertex, int *f, int *r) { if(*r==MAX-1) { cout<<"\n Queue Overflow."; exit(0); } (*r)++; a[*r]=vertex; if(*f==-1) *f=0; } int graph::deletequeue(int *a,int *f, int *r) { int data; if(*f==-1) { cout<<"\nQueue Underflow."; exit(0); } data=a[*f]; if(*f==*r) *f=*r=-1; else (*f)++; return data; } int graph::isempty(int *f) { if(*f==-1) return TRUE; return FALSE; } void graph::del(node *n) { node *temp; while(n!=NULL) { temp=n->next; delete n; n=temp; } E. Vijaya Kumar, M. Tech, M.I.S.T.E.

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} void main() { node *arr[MAX]; node *v1,*v2,*v3,*v4; graph g; clrscr(); cout<<"Graph before deletion\n"; v1=g.getnode_write(2); arr[0]=v1; v1->next=v2=g.getnode_write(3); v2->next=NULL; v1=g.getnode_write(1); arr[1]=v1; v1->next=v2=g.getnode_write(4); v2->next=v3=g.getnode_write(5); v3->next=NULL; v1=g.getnode_write(1); arr[2]=v1; v1->next=v2=g.getnode_write(6); v2->next=v3=g.getnode_write(7); v3->next=NULL; v1=g.getnode_write(2); arr[3]=v1; v1->next=v2=g.getnode_write(8); arr[4]=v1; v1->next=v2=g.getnode_write(8); v2->next=NULL; v1=g.getnode_write(3); arr[5]=v1; v1->next=v2=g.getnode_write(8); v2->next=NULL; v1=g.getnode_write(3); arr[6]=v1; v1->next=v2=g.getnode_write(8); v2->next=NULL; v1=g.getnode_write(4); arr[7]=v1; v1->next=v2=g.getnode_write(5); v2->next=v3=g.getnode_write(6); v3->next=v4=g.getnode_write(7); v4->next=NULL; cout<
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getch(); } OUTPUT: Graph before deletion

11)

1 2 3 4 5 6 7 8 Graph after deletion Write a C++ program to implement the Merge sort AIM: To implement a c++ program for one of the sorting technique. ALGORITHM: I. Merge (k, first, second, third): 1. Initialization of the variables f = first s = second i=0 2. Repeat while (f= second) then repeat while (s<=third) { i = i +1 temp [i] = k[s] s=s+1 } else repeat while (f< second) { i =i + 1 temp[i] = k[f] f=f+1


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} 4. get back the elements from the temporary elements repeat for i = 1 to n do k [first – 1 + i] = temp [i] 5. return PROGRAM: #include #include class merges { public: void msort(int,int *,int,int *,int *); void bsort(int,int *); }; void merges::bsort(int n,int a[]) { int flag=1; for(int j=0;ja[k+1]) { int temp=a[k]; a[k]=a[k+1]; a[k+1]=temp; flag=0; }} if(flag) break; else flag=1; } cout<<"\nentered list is \n"; cout<<"\nascending order\n"; for(int i=0;i
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if(a[i]b[j]) { c[k]=b[j]; j++; k++; } else { c[k]=a[i]; i++;j++;k++; } cout<>n; cout<<"\nenter elements \n"; E. Vijaya Kumar, M. Tech, M.I.S.T.E.

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for(i=0;i>a[i]; ms.bsort(n,a); cout<<"\nenter m value\n"; cin>>m; cout<<"\nenter elements\n"; for(i=0;i>b[i]; ms.bsort(m,b); ms.msort(n,a,m,b,c); getch(); OUTPUT: enter n value 5 enter elements 1 4 23 12 56 entered list is ascending order 1 4 12 23 56 enter m value 3 enter elements 13 12 1 entered list is ascending order 1 12 13 MERGED ARRAY IS 1 14 1 4 12 1 4 12 13 1 4 12 13 23 23 E. Vijaya Kumar, M. Tech, M.I.S.T.E.

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1 4 12 13 23 23

12)

Write a C++ program to implement the Heap sort AIM: A C++ program to implement Heap Sort ALGORITHM: I. heapSort(a, count) 1. end := count - 1 2. while end > 0 do 3. swap the root(ma value) of the heap with the last element of the

heap) 4.

swap(a[end], a[0]) decrease the size of the heap by one so that the previous max value

5. 6. 7.

stay in its proper placement) end := end - 1 (put the heap back in max-heap order) siftDown(a, 0, end)

will

II.heapify(a,count) 1. 2. 3. 4.

5. 6. 7.

(start is assigned the index in a of the last parent node) start := (count - 1) / 2 while start ≥ 0 do (sift down the node at index start to the proper place such that all nodes below the start index are in heap order) siftDown(a, start, count-1) start := start – 1 (after sifting down the root all nodes/elements are in heap order)

III.siftDown(a, start, end) 1. 2.

3. 4. 5.

6. 7.

root := start while root * 2 + 1 ≤ end do (While the root has at least one child) child := root * 2 + 1 (root*2+1 points to the left child) (If the child has a sibling and the child's value is less than its sibling's...) if child < end and a[child] < a[child + 1] then child := child + 1 (... then point to the right child instead)


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if a[root] < a[child] then (out of max-heap order) 9. swap(a[root], a[child]) (repeat to continue sifting down the child 10. root := child now) 11. else 12. return 8.

PROGRAM: #include #include void hsort(int x[],int n) { int i,elt,s,f,ivalue; for(i=1;i0 && (x[f]0;i--) {ivalue=x[i]; x[i]=x[0]; f=0; if(i==1) s=-1; else s=1; if((i>2) && (x[2]>x[1])) s=2; while((s>=0) && (ivaluei-1) s=-1; E. Vijaya Kumar, M. Tech, M.I.S.T.E.

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} x[f]=ivalue; }} void main() { int i,size,a[10]; clrscr(); cout<<"enter the size\n"; cin>>size; cout<<"enter elements\n"; for(i=0;i>a[i]; hsort(a,size); cout<<"sorted array \n"; for(i=0;i

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13)

Write a C++ program to perform the following operations a. Insertion int a B-Tree b. Deletion from a B-Tree

AIM: A C++ Program to perform insertion and deletion on BTree ALGORITHM:

I.B-Tree-Insert(T, k) 1. r <- root[T] 2. if n[r] = 2t - 1 a. then s <- Allocate-Node() b.root[T] <- s c. leaf[s] <- FALSE d.n[s] <- 0 e. c1 <- r f. B-Tree-Split-Child(s, 1, r) g. B-Tree-Insert-Nonfull(s, k) h.else B-Tree-Insert-Nonfull(r, k) II. B-Tree-Delete(x, k) 1.

if x is a leaf then

if k is in x then 3. delete k from x and return true 4. else return false //k is not in subtree 2.

5.

else //x is an internal node

if k is in x then 7. y = the child of x that precedes k if y has at least t keys then a. b. k' = the predecessor of k (use B-TreeFindLargest) c. Copy k' over k //i.e., replace k with k' B-Tree-Delete(y, k') //Note: recursive call 8. else //y has t-1 keys 9. z = the child of x that follows k 10. if z has at least t keys then 11. k' = the successor of k 12. Copy k' over k //i.e., replace k with k' 13. B-Tree-Delete(z, k') //Note: recursive call 14. stop 6.


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PROGRAM: #include #include class btre { struct node { node *left; char data; node *right; }*root; char *a; int *lc;int *rc; public: btre(char *,int *l,int *r,int size); void insert(int index); static node *create(char *a1,int *l,int *r,int index); void display(); static void inorder(node *sr); ~btre(); static void del(node *sr); }; btre::btre(char *a1,int *l,int *r,int size) { root=NULL; a=new char[size]; lc=new int[size]; rc=new int[size]; for(int i=0;ileft=create(a1,l,r,*(l+index)); temp->data=*(a1+index); temp->right=create(a1,l,r,*(r+index)); } E. Vijaya Kumar, M. Tech, M.I.S.T.E.

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return temp; } void btre::display() { inorder(root); } void btre::inorder(node *sr) { if(sr!=NULL) { inorder(sr->left); cout<data<<"\t"; inorder(sr->right); }} btre::~btre() { delete a; delete lc; delete rc; del(root); } void btre::del(node *sr) { if(sr!=NULL) { del(sr->left); del(sr->right); } delete sr; } void main() { char a1[15]; int l[15]; int r[15]; int sz; clrscr(); cout<< "enter the size\n"; cin>>sz; int sz1=sizeof(sz); cout<<"enter the elements \n"; for(int i=0;i>a1[i];} btre bt(a1,l,r,sz); bt.insert(0); cout<<"\n in-order traversal : "<
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OUTPUT: Enter size of the tree 6 enter elements 12 56 232 45 56 67 78 Btree before deletion 12 45 56 56 67 67

78

Binary tree after delete 12 45 56 56 78 n

232

14)

232

enter deleting elem

do you want delete ?

Write a C++ program to perform the following operations a. Insertion into an AVL Tree b. Deletion from an AVL Tree


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AIM: A C++ program to implement AVL Trees. ALGORITHM: I. INSERT: 1

Do Binary Search Tree Insert (recursive algorithm)

2

While the recursion returns, keep track of node p, p's child q and p's grandchild r within the path from inserted node to p.

a. b. c.

3

If p is unbalanced, do one of the following rotations: a. b. c. d.

if (p.left == q) and (p.left.left == r ), single rotation right in p; if (p.right == q ) and (p.right.right == r ), single rotation left in p; if (p.left == q) and (p.left.right == r ), LR-double rotation in p; or if (p.right == q ) and (p.right.left == r ), RL-double rotation in p.

II. DELETE: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18.

Let ptr, p be a reference to a Node. ptr = find(X If ptr is not null, Decrement elementCount; If ptr == root Set root to null and return If ptr is a leaf node, p = ptr.parent Set p's left/right child to null. Else If ptr is a node with 1 child (left/right), p = ptr.parent; Set p's left/right child to be ptr's left/right child. Else Let ptr2 be a Node*. ptr2 = findMin(ptr.right); ptr.element = ptr2.element; p = ptr2.parent Set p's left child to be ptr2's right child.

PROGRAM:


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#include #include #define FALSE 0 #define TRUE 1 struct AVLNode { int data ; int balfact ; AVLNode *left ; AVLNode *right ; }; class avltree { private : AVLNode *root ; public : avltree( ) ; AVLNode* insert ( int data, int *h ) ; static AVLNode* buildtree ( AVLNode *root, int data, int *h ) ; void display( AVLNode *root ) ; AVLNode* deldata ( AVLNode* root, int data, int *h ) ; static AVLNode* del ( AVLNode *node, AVLNode* root, int *h ) ; static AVLNode* balright ( AVLNode *root, int *h ) ; static AVLNode* balleft ( AVLNode* root, int *h ) ; void setroot ( AVLNode *avl ) ; ~avltree( ) ; static void deltree ( AVLNode *root ) ; }; // initialises data member avltree :: avltree( ) { root = NULL ; } // inserts an element in a binary tree by calling buildtree AVLNode* avltree :: insert ( int data, int *h ) { root = buildtree ( root, data, h ) ; return root ; E. Vijaya Kumar, M. Tech, M.I.S.T.E.

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} // inserts an element into tree AVLNode* avltree :: buildtree ( AVLNode *root, int data, int *h ) { AVLNode *node1, *node2 ; if ( root == NULL ) { root = new AVLNode ; root -> data = data ; root -> left = NULL ; root -> right = NULL ; root -> balfact = 0 ; *h = TRUE ; return ( root ) ; } if ( data < root -> data ) { root -> left = buildtree ( root -> left, data, h ) ; // If left subtree is higher if ( *h ) { switch ( root -> balfact ) { case 1 : node1 = root -> left ; if ( node1 -> balfact == 1 ) { cout << "\nRight rotation." ; root -> left = node1 -> right ; node1 -> right = root ; root -> balfact = 0 ; root = node1 ; } else { cout << "\nDouble rotation, left then right." ; node2 = node1 -> right ; node1 -> right = node2 -> left ; node2 -> left = node1 ; root -> left = node2 -> right ; E. Vijaya Kumar, M. Tech, M.I.S.T.E.

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node2 -> right = root ; if ( node2 -> balfact == 1 ) root -> balfact = -1 ; else root -> balfact = 0 ; if ( node2 -> balfact == -1 ) node1 -> balfact = 1 ; else node1 -> balfact = 0 ; root = node2 ; } root -> balfact = 0 ; *h = FALSE ; break ; case 0 : root -> balfact = 1 ; break ; case -1 : root -> balfact = 0 ; *h = FALSE ; } } } if ( data > root -> data ) { root -> right = buildtree ( root -> right, data, h ) ; // If the right subtree is higher if ( *h ) { switch ( root -> balfact ) { case 1 : root -> balfact = 0 ; *h = FALSE ; break ; case 0 :


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root -> balfact = -1 ; break ; case -1 : node1 = root -> right ; if ( node1 -> balfact == -1 ) { cout << "\nLeft rotation." ; root -> right = node1 -> left ; node1 -> left = root ; root -> balfact = 0 ; root = node1 ; } else { cout << "\nDouble rotation, right then left." ; node2 = node1 -> left ; node1 -> left = node2 -> right ; node2 -> right = node1 ; root -> right = node2 -> left ; node2 -> left = root ; if ( node2 -> balfact == -1 ) root -> balfact = 1 ; else root -> balfact = 0 ; if ( node2 -> balfact == 1 ) node1 -> balfact = -1 ; else node1 -> balfact = 0 ; root = node2 ; } root -> balfact = 0 ; *h = FALSE ; } } } return ( root ) ; } // prints data void avltree :: display ( AVLNode* root ) { if ( root != NULL ) { E. Vijaya Kumar, M. Tech, M.I.S.T.E.

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display ( root -> left ) ; cout << root -> data << "\t" ; display ( root -> right ) ; } } // To delete an item from the tree AVLNode* avltree :: deldata ( AVLNode *root, int data, int *h ) { AVLNode *node ; if ( root -> data == 13 ) cout << root -> data ; if ( root == NULL ) { cout << "\nNo such data." ; return ( root ) ; } else { if ( data < root -> data ) { root -> left = deldata ( root -> left, data, h ) ; if ( *h ) root = balright ( root, h ) ; } else { if ( data > root -> data ) { root -> right = deldata ( root -> right, data, h ) ; if ( *h ) root = balleft ( root, h ) ; } else { node = root ; if ( node -> right == NULL ) { root = node -> left ; *h = TRUE ; delete ( node ) ; } else { if ( node -> left == NULL ) E. Vijaya Kumar, M. Tech, M.I.S.T.E.

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{ root = node -> right ; *h = TRUE ; delete ( node ) ; } else { node -> right = del ( node -> right, node, h); if ( *h ) root = balleft ( root, h ) ; } } } } } return ( root ) ; } AVLNode* avltree :: del ( AVLNode *succ, AVLNode *node, int *h ) { AVLNode *temp = succ ; if ( succ -> left != NULL ) { succ -> left = del ( succ -> left, node, h ) ; if ( *h ) succ = balright ( succ, h ) ; } else { temp = succ ; node -> data = succ -> data ; succ = succ -> right ; delete ( temp ) ; *h = TRUE ; } return ( succ ) ; } // To balance the tree, if right sub-tree is higher AVLNode* avltree :: balright ( AVLNode *root, int *h ) { AVLNode *temp1, *temp2 ; switch ( root -> balfact ) { E. Vijaya Kumar, M. Tech, M.I.S.T.E.

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case 1 : root -> balfact = 0 ; break ; case 0 : root -> balfact = -1 ; *h = FALSE ; break ; case -1 : temp1 = root -> right ; if ( temp1 -> balfact <= 0 ) { cout << "\nLeft rotation." ; root -> right = temp1 -> left ; temp1 -> left = root ; if ( temp1 -> balfact == 0 ) { root -> balfact = -1 ; temp1 -> balfact = 1 ; *h = FALSE ; } else { root -> balfact = temp1 -> balfact = 0 ; } root = temp1 ; } else { cout << "\nDouble rotation, right then left." ; temp2 = temp1 -> left ; temp1 -> left = temp2 -> right ; temp2 -> right = temp1 ; root -> right = temp2 -> left ; temp2 -> left = root ; if ( temp2 -> balfact == -1 ) root -> balfact = 1 ; else root -> balfact = 0 ; if ( temp2 -> balfact == 1 ) E. Vijaya Kumar, M. Tech, M.I.S.T.E.

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temp1 -> balfact = -1 ; else temp1 -> balfact = 0 ; root = temp2 ; temp2 -> balfact = 0 ; } } return ( root ) ; } // To balance the tree, if left sub-tree is higher AVLNode* avltree :: balleft ( AVLNode *root, int *h ) { AVLNode *temp1, *temp2 ; switch ( root -> balfact ) { case -1 : root -> balfact = 0 ; break ; case 0 : root -> balfact = 1 ; *h = FALSE ; break ; case 1 : temp1 = root -> left ; if ( temp1 -> balfact >= 0 ) { cout << "\nRight rotation." ; root -> left = temp1 -> right ; temp1 -> right = root ; if ( temp1 -> balfact == 0 ) { root -> balfact = 1 ; temp1 -> balfact = -1 ; *h = FALSE ; } else { root -> balfact = temp1 -> balfact = 0 ; E. Vijaya Kumar, M. Tech, M.I.S.T.E.

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} root = temp1 ; } else { cout << "\nDouble rotation, left then right." ; temp2 = temp1 -> right ; temp1 -> right = temp2 -> left ; temp2 -> left = temp1 ; root -> left = temp2 -> right ; temp2 -> right = root ; if ( temp2 -> balfact == 1 ) root -> balfact = -1 ; else root -> balfact = 0 ; if ( temp2-> balfact == -1 ) temp1 -> balfact = 1 ; else temp1 -> balfact = 0 ; root = temp2 ; temp2 -> balfact = 0 ; } } return ( root ) ; } // sets new the root node void avltree :: setroot ( AVLNode *avl ) { root = avl ; } // calls deltree to deallocate memory avltree :: ~avltree( ) { deltree ( root ) ; } // deletes the tree void avltree :: deltree ( AVLNode *root ) { if ( root != NULL ) E. Vijaya Kumar, M. Tech, M.I.S.T.E.

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{ deltree ( root -> left ) ; deltree ( root -> right ) ; } delete ( root ) ; } void main( ) { avltree at ; AVLNode *avl = NULL ; int h ; avl = at.insert ( 20, &h ) ; at.setroot ( avl ) ; avl = at.insert ( 6, &h ) ; at.setroot ( avl ) ; avl = at.insert ( 29, &h ) ; at.setroot ( avl ) ; avl = at.insert ( 5, &h ) ; at.setroot ( avl ) ; avl = at.insert ( 12, &h ) ; at.setroot ( avl ) ; avl = at.insert ( 25, &h ) ; at.setroot ( avl ) ; avl = at.insert ( 32, &h ) ; at.setroot ( avl ) ; avl = at.insert ( 10, &h ) ; at.setroot ( avl ) ; avl = at.insert ( 15, &h ) ; at.setroot ( avl ) ; avl = at.insert ( 27, &h ) ; at.setroot ( avl ) ; avl = at.insert ( 13, &h ) ; at.setroot ( avl ) ; cout << endl << "AVL tree:\n" ; at.display ( avl ) ; avl = at.deldata ( avl, 20, &h ) ; at.setroot ( avl ) ; avl = at.deldata ( avl, 12, &h ) ; at.setroot ( avl ) ; cout << endl << "AVL tree after deletion of a node:\n" ; at.display ( avl ) ; } E. Vijaya Kumar, M. Tech, M.I.S.T.E.

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OUTPUT: Enter your choice 1 enter the size 1 14 MENU 1. Insert 2. Search 3. Delete 4. Display 5. Quit Enter your choice 5 Sorry Left rotation. AVL tree: 5 6 10 12 13 15 20 32 AVL tree after deletion of a node: 5 6 10 13 15 25 27 Left rotation. AVL tree: 5 6 10 12 13 15 20

25

27

29

32

25

27

29

29

15) Write a C++ program to implement kruskal’s algorithm to generate a minimum cost spanning tree AIM: A c++ program to perform Kruskals algorithm to generate minimum cost spanning trees. ALGORITHM: I. Short_path ( )


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1. start 2. set s[0] = 1, dist[0] = 0 3. repeat steps v = 1 to v = nov i. steps set s[v] = 0 ii. set dist [v] = c[0] [v] 4. repeat steps i = 1 to i < nov i. set min = 999 ii. repeat step w = 1 to w < nov iii. a. if (s[w] == 0) then i. if (dist [w] < min) set v = w min = dist[w]. b. s[v] = 1 iv. repeat step w = 1 to w< nov i. if (s[w] ==0) then if (min + c[v][w] < dist [w]) dist[w] = min + c[v][w] 5. end PROGRAM: #include #include struct edge { int v1,v2,wt; }; struct edge ed[20]; int A[20],v,e; int getedges(struct edge ed[20]) { char c='y'; int p,v1,v2,wt; e=0; cout <<"Enter value of edges \n"; cin>>p; while(c!='n') { e++; cout<<"Enter v1,v2,wt\n"; cin>>v1>>v2>>wt; ed[e].v1=v1; ed[e].v2=v2; ed[e].wt=wt; cout<<"Read 9999 to stop\n"; cin>>c; } E. Vijaya Kumar, M. Tech, M.I.S.T.E.

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cout<<"Edges= "<temp.wt) { ed[j]=ed[j-1]; j--;} ed[j]=temp;}} initi(int A[20],int v) { int i; {for(i=1;i0) { i=A[i];} while(A[j]>0) { j=A[j];} if (i!=j) { A[j]=i; cout<<"\n"; cout<
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i=ed[edind].v1; j=ed[edind].v2; findunion(A,i,j); } while(eds>v; e=getedges(ed); sorted(ed,e); initi(A,v); cout<<"\nKruskals Spanning Tree Edge=\n"; krusk(ed,v); getch(); }

OUTPUT: Enter the no. of vertices 3 Enter value of edges 12 Enter v1,v2,wt 12 13 4 Read n to stop 12 Enter v1,v2,wt 13 14 Read n to stop E. Vijaya Kumar, M. Tech, M.I.S.T.E.

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2 Enter v1,v2,wt 34 35 5 Read n to stop n Edges= 3 Kruskals Spanning Tree Edge= 12to13 34to35 2to13

16) Wite a C++ program to implement Prim’s algorithm to generate a minimum cost spanning tree AIM: To write a c++ program to implement prims algorithm to generate minimum spanning tree. ALGORITHM: 1. start 2. for i equal to 0 to no do 3. selected [i] = false 4. end 5. for i is equal to 1 to n do 6. for j is equal to 1 to n do 7. tree [i][j] = q 8. end for E. Vijaya Kumar, M. Tech, M.I.S.T.E.

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9. end for 10. selected [i] = true, ne = 1 11. while (ne cptr [i][j]) 7. min = cptr [i][j] 8. x< - i, y <-j 9. end if 12. tree[x][y] = 1 13. selected [y] = true 14. ne ++ 15. return [tree] 16, end PROGRAM: #include #include const int MAX=5; struct lledge { int v1,v2; float cost; lledge *next; }; int stree[MAX]; int count[MAX]; int mincost; lledge *create(int cr1,int vr2,int cs); lledge *kminstree(lledge *root,int n); int getrval(int i); void combine(int i,int j); void del(lledge *root); lledge *kminstree(lledge *root,int n) { lledge *temp=NULL; lledge *p,*q; int noe=0; int i,p1,p2; for(i=0;i
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for(i=0;inext; p1=getrval(p->v1); p2=getrval(p->v2); if(p1!=p2) { combine(p->v1,p->v2); noe++; mincost+=p->cost; if(temp==NULL) { temp=p; q=temp; } else { q->next=p; q=q->next; } q->next=NULL; }} return temp; } int getrval(int i) { int j,k,temp; k=i; while(stree[k]!=k) k=stree[k]; j=i; while(j!=k) { temp=stree[j]; stree[j]=k; j=temp; } return k; } void combine(int i,int j) { if(count[i]
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if(count[i]==count[j]) count[j]++; }} void del(lledge *root) { lledge *temp; while(root!=NULL) { temp=root->next; delete root; root=temp; }} void main() { lledge *temp,*root; int i; root= new lledge; clrscr(); root->v1=4; root->v2=3; root->cost=1; temp=root->next=new lledge; temp=temp->next; temp->v1=4; temp->v2=2; temp->cost=2; temp->next=new lledge; temp=temp->next; temp->v1=3; temp->v2=2; temp->cost=3; temp->next=new lledge; temp=temp->next; temp->v1=4; temp->v2=1; temp->cost=4; temp->next=new lledge; root=kminstree(root,MAX); for(i=1;i"<

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OUTPUT: stree 1j->4 stree 2j->4 stree 3j->4 stree 4j->4 the min cost of spanning tree is 7 after deleting

17)Write a C++ program to implement all the functions of a dictionary (ADT) using hashing. AIM: A C++ Program to implement dictionary (ADT) using hashing PROGRAM: #include #include #include void init(int h[]); void insert(int h[],int); void search(int h[],int); void Delete(int h[],int); void disp(); void insert(int h[],int a) { int r,i; r=a%10; E. Vijaya Kumar, M. Tech, M.I.S.T.E.

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i=r; if(h[i]==0) h[i]=a; else i--; h[i]=a; } void search(int h[],int key) { int i,r; r=key%10; while(h[r]!=0) { if(h[r]==key) {cout<<"found"; break; } else r--; if(h[r]!=key) cout<<"not found"; } } void init(int h[]) { int i; for(i=0;i<10;i++) h[i]=0; } void Delete(int h[],int e) { int i,r; r=e%10; while(h[r]!=0) { if(h[r]==e) {cout<<"found"; h[r]=0;break; } else r--; if(h[r]!=e) cout<<"not found"; }} void disp(int h[]) { int i; cout<<"Array is \n"; E. Vijaya Kumar, M. Tech, M.I.S.T.E.

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for(i=0;i<10;i++) { cout<>ch; switch(ch) { case 1: { cout<<"enter the size\n"; cin>>size; for(i=0;i>a; insert(h,a); }break;} case 2: { cout<<"Enter the element to be searched\n"; cin>>key; search(h,key); break; } case 3: { cout<<"Enter the element to be deleted\n"; cin>>a; Delete(h,a); break; } case 4: { disp(h); E. Vijaya Kumar, M. Tech, M.I.S.T.E.

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break; } default: cout<<"Sorry\n"; }}while(ch!=5); getch(); } OUTPUT: MENU 1. Insert 2. Search 3. Delete 4. Display 5. Quit Enter your choice 1 enter the size 2 13 12

MENU 1. Insert 2. Search 3. Delete 4. Display 5. Quit Enter your choice 4 Array is 0 0 12 13 0 0 0 0 0 0 MENU 1. Insert 2. Search 3. Delete E. Vijaya Kumar, M. Tech, M.I.S.T.E.

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